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Problem Given that u = i ^ − 2 j ^ + 3 k ^ \mathbf{u} = \hat{i} - 2\hat{j} + 3\hat{k} u = i ^ − 2 j ^ + 3 k ^ v = 2 i ^ + j ^ + 4 k ^ \mathbf{v} = 2\hat{i} + \hat{j} + 4\hat{k} v = 2 i ^ + j ^ + 4 k ^ w = i ^ + 3 j ^ + 3 k ^ \mathbf{w} = \hat{i} + 3\hat{j} + 3\hat{k} w = i ^ + 3 j ^ + 3 k ^ ( u ⋅ R − 15 ) i ^ + ( v ⋅ R − 30 ) j ^ + ( w ⋅ R − 20 ) k ^ = 0 (\mathbf{u} \cdot \mathbf{R} - 15)\hat{i} + (\mathbf{v} \cdot \mathbf{R} - 30)\hat{j} + (\mathbf{w} \cdot \mathbf{R} - 20)\hat{k} = \mathbf{0} ( u ⋅ R − 15 ) i ^ + ( v ⋅ R − 30 ) j ^ + ( w ⋅ R − 20 ) k ^ = 0 ∣ R ∣ |\mathbf{R}| ∣ R ∣ Browse the problem library